Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
640 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#11745162 | C2 | direct (N × H) |
| 14. #11745162 | C22 | direct (N × H) |
| 21. C22×Dic29 | C8 | semidirect |
| 40. C2×Dic29 | C2×C8 | semidirect |
| 46. C22×C29 | C4⋊C8 | semidirect |
| 55. Dic29 | C22×C8 | semidirect |
| 60. C2×C29 | C2×C4⋊C8 | semidirect |
| 74. C29 | C22×C4⋊C8 | semidirect |
| 105. C22 | #11745162 | direct (N × H) |
| 115. C2 | C2×#11745162 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6597 | 2 |
| C22×C4×Dic29 | 2 |
| C2×#11745162 | 2 |
| C23×C8×C29 | 2 |
| C22×C4⋊C8 | 29 |